arXiv subjects

Stephen J. Curran

Publications and source records attributed to Stephen J. Curran.

17 recordsLinked to original sources

arXiv2026

Floridian Solitaire: A New Variant of Bulgarian Solitaire

Bulgarian solitaire is a well-studied, no-choice, no-loss, one-player game involving stacks of cards. More formally, it is a self-map on the set of partitions of a fixed integer $n.$ As a finite dynamical system, its long-term behavior is well understood. Every trajectory ends in a cycle. The partitions that are in a cycle are parameterized by binary vectors, and the cycles by binary necklaces. Call a partition separated if distinct part sizes differ by at least two. The vast majority of partitions belonging to a cycle are not separated. Motivated by this fact, we consider a variant where the player has choices, but is restricted to separated partitions and, if unable to make a legal move, may lose. We prove that for $n>73$, there are cycles, and hence winning initial positions. We analyze the game for small values of $n$ and describe computations which, together with our main result, show that there are cycles for $n \in \{2,6,8,11,14,16,18,21\}$ and for $n \ge 23$, but for no other $n.$

math.CO↗

arXiv2026

A search for HI absorption in distant star-forming galaxies with ASKAP-FLASH - II. Direct observations and stacking of 21 cm line

We present results of a search for associated and intervening HI 21 cm absorption in star-forming galaxies and a control sample of radio galaxies at 0.4 < $z$ < 1.0, using ASKAP's FLASH HI 21 cm absorption survey. We report the detection of a new HI 21 cm absorption line in radio galaxy NVSS J214954-004657 at $z_{\mathrm{HI}}$ = 0.863. Additionally, we present results of HI 21 cm stacking for associated and intervening star-forming and radio galaxy catalogues. For the first time at these redshifts, we report tentative detections of stacked HI 21 cm absorption for associated galaxies when stacked in order of descending radio source brightness, and show that these tentative detections become buried as optical depth increases as progressively weaker sources are co-added into the stack. No stacked signal is detected when co-adding intervening galaxy spectra. We speculate that the ability to detect a stacked HI 21 cm detection is dependent on the background source optical depth limits, as well as source covering factors. Covering factor has a greater impact when stacking intervening systems, and can be considered to effectively weaken the observed flux density of a radio source. We find no significant difference in detection rate for associated HI 21 cm absorption in star-forming galaxies versus the general radio-source population at the same redshift. Although detection rates are low, from a meta-analysis of HI 21 cm surveys we find that 1 detection is expected given the survey parameters.

astro-ph.GA↗

arXiv2026

Two-pile and three-pile games of a new variant of Nim known as Halve Nim

We investigate a variant of Nim called Halve Nim, which in addition to the standard moves of Nim, we allow replacing each pile of coins with half its amount. We determine the P-positions of all two-pile games of Halve Nim. Also, we determine the P-positions of all three-pile games of Halve Nim in which one pile has at most ten coins.

math.CO↗

arXiv2026

C4-face-magic labeling on a 4x4 Klein bottle grid graph

For a graph G = (V, E) embedded in the Klein bottle, let F(G) denote the set of faces of G. A C_4-face-magic Klein bottle labeling on G is a bijection f: V(G) to {1, 2,..., |V(G)|} such that for any F in F(G) with F isomorphic C_4, the sum of all the vertex labelings along C_4 is a constant. We say that a C_4-face-magic labeling X={x_{i,j} : 0< i,j< 5} on the 4x4 Klein bottle grid graph is horizontally (or vertically) pairwise balanced if x_{2i-1,j} + x_{2i,j}=17 for 0< i <3 and 0< j \le <5 (or x_{i,2j-1} + x_{i2,j}=17 for 0< i <5 and 0< j <3). We show that the 4x4 Klein bottle grid graph has 192 C_4-face-magic labelings up to symmetries on a Klein bottle. We classify these labelings into two categories depending on whether a C_4-face-magic label preserving permutation of the labeling is either horizontally pairwise balanced or vertically pairwise balanced. These results extend known results on C_4-face-magic labelings on an mxn Klein bottle grid graph.

math.CO↗

arXiv2026

A jet-gas interaction beyond the host galaxy: detection of a neutral hydrogen outflow at cosmic noon

We present upgraded Giant Metrewave Radio Telescope (uGMRT) observations of 0731+438, an \mbox{FR II} radio galaxy at a redshift of 2.429 with two lobes separated by 82 kpc. A blueshifted, faint and broad \mbox{H{\sc i}} 21 cm absorption line with velocity full width at half maximum (FWHM) $\sim 600\,\rm km\,s^{-1}$ is detected against the southern radio lobe that is 47 kpc from radio core, indicating a neutral hydrogen outflow associated with jet-gas interaction beyond the host galaxy. The outflow has a mass outflow rate of $\sim\,0.4T_{\rm s}\Omega\rm\, M_\odot\,{\rm yr}^{-1}$, which could increase to $\sim\,4.0T_{\rm s}\Omega\rm\,M_\odot\,{\rm yr}^{-1}$, corresponding to an energy outflow rate of $2.4T_{\rm s}\Omega\times10^{40}$ -- $1.5T_{\rm s}\Omega\times10^{41}\,\rm erg\,s^{-1}$, where $T_{\rm s}$ is the spin temperature and $\Omega$ is the solid angle of the outflow. Previous optical observations identified an extended emission line region aligned with the radio axis, ionized by the central Active Galactic Nucleus (AGN). Within this region, a warm and ionized outflow with a mass outflow rate of $\sim\,50\rm\, M_\odot\,{\rm yr}^{-1}$ and an energy outflow rate of $\sim1.7\times10^{43}\,\rm erg\,s^{-1}$ was detected. We propose that both the extended emission line region and the optical outflow are results of synergistic effect between jet and AGN radiation. The AGN likely exerts negative feedback on the host galaxy, as evidenced by the gas expulsion by the jet and the high velocity dispersion of ionized gas observed optically. So far, detections of jet-driven neutral hydrogen outflows remain rare. The high redshift, large outflow radii, substantial mass outflow rate and energy outflow rate of the neutral hydrogen outflow in 0731+438 expand the known parameter space of such outflows.

astro-ph.GA↗

arXiv2025

A stringent constraint on the fractional change of proton g-factor

We report a constraint on the cosmological variation of the proton g-factor, $g_p$. By comparing the measured redshifts between \mbox{H\,{\sc i}} 21 cm and OH 18 cm lines observed with the newly commissioned Five-hundred-meter Aperture Spherical radio Telescope (FAST) toward PKS 1413+135 at $z$ = 0.24671, we obtain $\Delta g_{p}/g_{p} = (-4.3\pm2.5)\times10^{-5}$, which is more than two orders of magnitude more sensitive than previous constraints. In addition, we obtain sensitive constraints of $\Delta (\mu\alpha^{2})/(\mu\alpha^{2}) = (2.0\pm1.2)\times10^{-5}$ and $\Delta (\mu\alpha^{2}g_{p}^{0.64})/(\mu\alpha^{2}g_{p}^{0.64}) = (-4.7\pm1.9)\times10^{-6}$.

astro-ph.CO↗

arXiv2025

Photometric Redshift Predictions with a Neural Network for DESI Quasars

Accurate redshift measurements are essential for studying the evolution of quasi-stellar objects (QSOs) and their role in cosmic structure formation. While spectroscopic redshifts provide high precision, they are impractical for the vast number of sources detected in large-scale surveys. Photometric redshifts, derived from broadband fluxes, offer an efficient alternative, particularly when combined with machine learning techniques. In this work, we develop and evaluate a neural network model for predicting the redshifts of QSOs in the Dark Energy Spectroscopic Instrument (DESI) Early Data Release spectroscopic catalogue, using photometry from DESI, the Widefield Infrared Survey Explorer (WISE) and the Galactic Evolution Explorer (GALEX). We compare the performance of the neural network model against a k-Nearest Neighbours approach, these being the most accurate and least resource-intensive of the methods trialled herein, optimising model parameters and assessing accuracy with standard statistical metrics. Our results show that incorporating ultraviolet photometry from GALEX improves photometric redshift estimates, reducing scatter and catastrophic outliers compared to models trained only on near infrared and optical bands. The neural network achieves a correlation coefficient with spectroscopic redshift of $0.9187$ with normalised median absolute deviation of $0.197$, representing a significant improvement over other methods. Our work combines DESI, WISE and GALEX measurements, providing robust predictions which address the difficulties in predicting photometric redshift of QSOs over a large redshift range.

astro-ph.GA↗

arXiv2025

New constraints on the values of the fundamental constants at a look-back time of 7.3 Gyr

The study of redshifted spectral lines can provide a measure of the fundamental constants over large look-back times. Current grand unified theories predict an evolution in these constants and astronomical observations offer the only experimental measure of the values of the constants over large timescales. Of particular interest are the dimensionless constants: the fine structure constant ($α$), the proton-electron mass ratio ($μ$), and the proton g-factor ($g_p$), since these do not require a "standard meterstick". Here we present a re-analysis of the 18 cm hydroxyl (OH) lines at $z=0.89$, which were recently detected with the MeerKAT telescope, toward the radio source PKS\,1830-211. Utilizing the previous constraint of $Δμ/μ=(-1.8\pm1.2)\times10^{-7}$, we obtain $Δ(αg_p^{0.27})/(αg_p^{0.27})\lesssim5.7\times10^{-5}$, $Δα/α\lesssim2.3\times10^{-3}$ , and $Δg_p/g_p\lesssim7.9\times10^{-3}$. These new constraints are consistent with no evolution over a look-back time of 7.3 Gyr and provide another valuable data point in the putative evolution of the constants.

astro-ph.CO↗

arXiv2025

The First Large Absorption Survey in HI (FLASH): II. Pilot Survey data release and first results

The First Large Absorption Survey in HI (FLASH) is a large-area radio survey for neutral hydrogen in the redshift range 0.4 1$, and appear to be a mixture of intervening and associated systems. Interestingly, around two-thirds of the lines found in this untargeted sample are detected against sources with a peaked-spectrum radio continuum, which are only a minor (5-20%) fraction of the overall radio-source population. The overall detection rate for HI absorption lines in the Pilot Surveys (0.3 to 0.5 lines per ASKAP field) is a factor of two below the expected value. One possible reason for this is the presence of a range of spectral-line artefacts in the Pilot Survey data that have now been mitigated and are not expected to recur in the full FLASH survey. A future paper will discuss the host galaxies of the HI absorption systems identified here.

astro-ph.GA↗

arXiv2025

Constraints on the fractional changes of the fundamental constants at a look-back time of 2.5 Myrs

The quantum nature of gravity remains one of the greatest mysteries of modern physics, with many unified theories predicting variations in fundamental constants across space and time. Here we present precise measurements of these variations at galactic dynamical timescales - a critical but previously unexplored regime. Using simultaneous observations of H \textsc{i} and OH lines in M31, we probe potential variations of fundamental constants at a lookback time of 2.5 million years. We obtained $Δ(μα^2g_p^{0.64})/(μα^2g_p^{0.64}) < 3.6 \times 10^{-6}$, with complementary constraints on $Δ(μα^2)/(μα^2) < 4.6 \times 10^{-3}$, and $Δg_p/g_p < 7.2 \times 10^{-3}$, where $α$ is the fine structure constant, $μ$ is the proton-electron mass ratio, and $g_p$ is the proton $g$-factor. These results bridge the gap between laboratory tests and cosmological observations, providing unique insights into the coupling between local dynamics and fundamental physics. Our findings challenge theories predicting significant variations over galactic timescales, while demonstrating a powerful new probe of quantum gravity models.

astro-ph.GA↗

arXiv2023

The FLASH pilot survey: an HI absorption search against MRC 1-Jy radio sources

We report an ASKAP search for associated HI 21-cm absorption against bright radio sources from the Molonglo Reference Catalogue (MRC) 1-Jy sample. The search uses pilot survey data from the ASKAP First Large Absorption Survey in \hi (FLASH) covering the redshift range $0.42 < z < 1.00$. From a sample of 62 MRC 1-Jy radio galaxies and quasars in this redshift range we report three new detections of associated HI 21-cm absorption, yielding an overall detection fraction of $1.8\%^{+4.0\%}_{-1.5\%}$. The detected systems comprise two radio galaxies (MRC 2216$-$281 at $z=0.657$ and MRC 0531$-$237 at $z=0.851$) and one quasar (MRC 2156$-$245 at $z=0.862$). The MRC 0531$-$237 absorption system is the strongest found to date, with a velocity integrated optical depth of $\rm 143.8 \pm 0.4 \ km \ s^{-1}$. All three objects with detected HI 21-cm absorption are peaked-spectrum or compact steep-spectrum (CSS) radio sources, classified based on our SED fits to the spectra. Two of them show strong interplanetary scintillation at 162 MHz, implying that the radio continuum source is smaller than 1 arcsec in size even at low frequencies. Among the class of peaked-spectrum and compact steep-spectrum radio sources, the HI detection fraction is $23\%^{+22\%}_{-13\%}$. This is consistent within $1σ$ with a detection fraction of $\approx 42\%^{+21\%}_{-15\%}$ in earlier reported GPS and CSS samples at intermediate redshifts ($0.4 < z < 1.0$). All three detections have a high 1.4 GHz radio luminosity, with MRC 0531$-$237 and MRC 2216$-$281 having the highest values in the sample, $\rm > 27.5 \ W \ Hz^{-1}$. The preponderance of extended radio sources in our sample could partially explain the overall low detection fraction, while the effects of a redshift evolution in gas properties and AGN UV luminosity on the neutral gas absorption still need to be investigated.

astro-ph.GA↗

arXiv2023

A Comment on Dean's Construction of Prime Labelings on Ladders

A prime labeling on a graph of order $m$ is an assignment of $\{ 1, 2, \ldots, m \}$ to the vertices of the graph such that each pair of adjacent vertices has coprime labels. The ladder of order $2n$ is the $2 \times n$ grid graph graph $P_2 \times P_n$. In a recent paper, Dean claimed a proof of the Prime Ladder Conjecture that every ladder has a prime labeling. We point out a flaw in Dean's construction, showing that a stronger hypothesis is needed for it to hold. We conjecture that this stronger hypothesis is true. We also offer an alternative construction inspired by Dean's approach which shows that if the Even Goldbach Conjecture and a particular strengthening of Lemoine's Conjecture are true then the Prime Ladder Conjecture follows.

math.CO↗

arXiv2022

Odd order $C_4$-face-magic $m \times n$ projective grid graphs having $C_4$-face-magic value $2mn+1$ or $2mn+3$

For a graph $G = (V, E)$ embedded in the projective plane, let $\mathcal{F}(G)$ denote the set of faces of $G$. Then, $G$ is called a $C_n$-face-magic projective graph if there exists a bijection $f: V(G) \to \{1, 2, \dots, |V(G)|\}$ such that for any $F \in \mathcal{F}(G)$ with $F \cong C_n$, the sum of all the vertex labels around $C_n$ is a constant $S$. We consider the $m \times n$ grid graph, denoted by $\mathcal{P}_{m,n}$, embedded in the projective plane in the natural way. Let $m \geqslant 3$ and $n \geqslant 3$ be odd integers. It is known that the $C_4$-face-magic value of a $C_4$-face-magic labeling on $\mathcal{P}_{m,n}$ is either $2mn+1$, $2mn+2$, or $2mn+3$. The characterization of $C_4$-face-magic labelings on $\mathcal{P}_{m,n}$ having $C_4$-face-magic value $2mn+2$ is known. In this paper, we determine a category of $C_4$-face-magic labelings on $\mathcal{P}_{m,n}$ for which the $C_4$-face-magic value is either $2mn+1$ or $2mn+3$. It is conjectured that these are the only $C_4$-face-magic labeling on $\mathcal{P}_{m,n}$ having $C_4$-face-magic value $2mn+1$ or $2mn+3$.

math.CO↗

arXiv2022

Equatorially balanced C4-face-magic labelings on Klein bottle grid graphs

For a graph $G = (V, E)$ embedded in the Klein bottle, let $\mathcal{F}(G)$ denote the set of faces of $G$. Then, $G$ is called a $C_k$-face-magic Klein bottle graph if there exists a bijection $f: V(G) \to \{1, 2, \dots, |V(G)|\}$ such that for any $F \in \mathcal{F}(G)$ with $F \cong C_k$, the sum of all the vertex labelings along $C_k$ is a constant $S$. Let $x_v =f(v)$ for all $v\in V(G)$. We call $\{x_v : v\in V(G)\}$ a $C_k$-face-magic Klein bottle labeling on $G$. We consider the $m \times n$ grid graph, denoted by $\mathcal{K}_{m,n}$, embedded in the Klein bottle in the natural way. We show that for $m,n\ge 2$, $\mathcal{K}_{m,n}$ admits a $C_4$-face-magic Klein bottle labeling if and only if $n$ is even. We say that a $C_4$-face-magic Klein bottle labeling $\{x_{i,j}: (i,j) \in V(\mathcal{K}_{m,n}) \}$ on $\mathcal{K}_{m,n}$ is equatorially balanced if $x_{i,j} + x_{i,n+1-j} = \tfrac{1}{2} S$ for all $(i,j) \in V(\mathcal{K}_{m,n})$. We show that when $m$ is odd, a $C_4$-face-magic Klein bottle labeling on $\mathcal{K}_{m,n}$ must be equatorially balanced. Also when $m$ is odd, we show that (up to symmetries on the Klein bottle) the number of $C_4$-face-magic Klein bottle labelings on the $m \times 4$ Klein bottle grid graph is $2^m \, (m-1)! \, τ(m)$, where $τ(m)$ is the number of positive divisors of $m$. Furthermore, let $m\ge 3$ be an odd integer and $n \ge 6$ be an even integer. Then, the minimum number of distinct $C_4$-face-magic Klein bottle labelings $X$ on $\mathcal{K}_{m,n}$ (up to symmetries on a Klein bottle) is either $(5\cdot 2^m)(m-1)!$ if $n \equiv 0\pmod{4}$, or $(6\cdot 2^m)(m-1)!$ if $n \equiv 2\pmod{4}$.

math.CO↗

arXiv2015

Cool Outflows and HI absorbers with SKA

HI 21-cm absorption spectroscopy provides a unique probe of the cold neutral gas in normal and active galaxies from redshift z > 6 to the present day. We describe the status of HI absorption studies, the plans for pathfinders/precursors, the expected breakthroughs that will be possible with SKA1, and some limitations set by the current design.

astro-ph.GA↗

arXiv2011

Cayley graphs of order 16p are hamiltonian

Suppose G is a finite group, such that |G| = 16p, where p is prime. We show that if S is any generating set of G, then there is a hamiltonian cycle in the corresponding Cayley graph Cay(G;S).

math.CO↗

arXiv2004

Cosmological Evolution of Heavy Element and Molecular Hydrogen Abundances

Spectroscopic observations of distant quasars have resulted in the detection of molecular hydrogen in intervening damped Lyman-alpha absorption clouds (DLAs). We use observations compiled from different experimental groups to show that the molecular hydrogen abundance exhibits a dramatic increase over a cosmological time period corresponding to 13% to 24% of the age of the universe. We also tentatively show that the heavy element abundances in the same gas clouds exhibit a faster and more well-defined cosmological evolution compared to the general DLA population over the same time baseline. We argue that this latter point is unsurprising, because the general DLA population arises in a wide variety of galaxy types and environments, and thus a spans broad range of ISM gas-phases and abundances at the same cosmic time. DLAs exhibiting H2 absorption may therefore circumvent this problem, efficiently identifying a narrower class of objects, and provide a more sensitive probe of cosmological chemical evolution.

astro-ph↗